Diffusion on Surfaces. 1. Effect of Concentration on the Diffusivity of Physically Adsorbed Gases Edwin R. Gilliland,' Raymond F. Baddour, George P. Perkinsorh2and Karl J. Sladek* Department of Chemical Engineering, Massachusetts lnstitute of Technology, Cambridge,
Mass. 02139
Surface transport is described in terms of the hopping of adsorbed molecules between adjacent sites of different adsorption strength. The change in surface diffusivity with surface concentration is attributed to a change in the strength of adsorption, as evidenced by a change in the differential heat of adsorption, q, with concentration. The correlating equation predicts that the surface diffusivity varies as exp(-aq/RT), where a is an experimental constant. New data on the flow of CO2, S02, and NH3 in porous glass are presented and are correlated successfully by the above equation. In addition, literature data for five other systems are correlated well by this method.
The diffusion and flow of gases through porous materials can occur by several different mechanisms. For solids with relatively narrow pore size distributions, several distinct regimes of behavior are observed, depending upon the ratio of the mean free path of gas molecules to the mean pore diameter. Knudsen flow (or diffusion) of nonadsorbed gas occurs a t large values of this ratio and is often encountered with high surface area materials a t moderate pressures. However, for gases which adsorb appreciably, flows of an unusually large magnitude, in comparison with the Knudsen flow of nonadsorbed gases, have been observed. These anomalously large transport rates can be attributed to the migration of adsorbed molecules along the internal surfaces of the porous solids. Since most microporous materials, such as adsorbents and catalysts, display strong adsorptive properties, an understanding of surface transport is important in characterizing the total transport of gases within these materials. Early investigators presented surface transport measurements in terms of a two-dimensional form of Fick's law dC N , = -bD," dx where N , is the flux in the x direction across a line of width b under the influence of a surface concentration gradient. However, in the earliest measurements of spreading of metals adsorbed on tungsten, D, was found to increase substantially with C, (see Barrer, 1941). The same effect is now known in a variety of physical adsorption systems, as recently reviewed by Horiguchi, et al. (1971). Barrer (1941) reviews theories attributing an increase of D, with C, to mutual repulsion of adsorbed species. Carman (1956) suggested that the change in D, with C, might be due to a distribution of binding energies on heterogeneous surfaces. Several attempts to improve the representation of surface transport are based on models different from Fick's law. Babbitt (1950) developed an equation which used the two-dimensional spreading pressure as transport potential. However, Carman (1956) noted that resulting transport coefficients still vary with C,. Gilliland, et al. (1958), presented a different equation which was also based on the spreading pressure gradient. Smith and Metzner (1964) showed that this equation did not agree with their transport data on physically adsorbed gases, if a constant
transport coefficient is required. Weaver and Metzner (1966) presented a detailed model involving calculation of trajectories of point molecules hopping along a smooth surface. Horiguchi, et al. (1971), showed that this did not satisfactorily represent their transport data on hydrocarbons in porous glass. The purpose of this two-part series of papers is to present a new model for the correlation of surface transport in both physical and chemical adsorption. The present paper focuses upon the details of the transport mechanism and the correlation of individual sets of data on transport of physically adsorbed material. Particular emphasis is placed on explaining the surface concentration dependence of the transport, and new data are reported covering the transport of COz, S O z , and NH3 in porous glass over a wide range of surface concentrations. In the following paper the correlation and prediction of the surface transport properties of different gas-solid systems is considered with particular emphasis on chemisorption. Transport Model DeBoer (1952, 1969) gives a vivid description of surface migration as a process in which adsorbed molecules hop between adjacent adsorption sites. These discrete sites correspond to definite positions in the surface lattice and arise from local variations in the binding energy along the surface. The strong temperature dependence of observed values of D, provides some evidence for the existence of these binding points; if no such sites were present, twodimensional gas behavior would occur and D, would be temperature-insensitive. Two-dimensional gas behavior is characterized by a surface mean free path A, that varies inversely with C, and that can exceed greatly the spacing between adjacent sites. This behavior is expected when the thermal energy for translation in two dimensions exceeds the energy barrier E for migration. If E is a fraction a of binding energy q, then the condition for gas-like behavior is
qfRT < l / a (2) At larger values of qIRT, A, is no longer controlled by collisions between adsorbed molecules. As q/RT increases, A, decreases to the spacing between adjacent sites and a hopping mechanism prevails. At small C, random walk diffusion of independent particles can be expected, with D, given by
' Deceased.
* American Cyanamid, Stamford, Conn. 06904.
(3)
Miilipore Corporation, Bedford. Mass. 01 730.
Ind. Eng. Chem., Fundam., Vol. 13, No. 2, 1974
95
where the jump frequency Y and jump distance A, are assumed independent of C,. As C, increases, self-encounters of migrating molecules become important. One possible result is that a molecule which encounters a filled site does not complete the jump but instead remains at its original site. This would cause D. to vanish at monolayer coverage. The opposite possibility would be for the migrating molecule to occupy a second layer temporarily. This would give an increase in D, near monolayer coverage since the second layer would be less strongly bound than the first. The lack of any unusual behavior of D, near monolayer coverage (shown later) indicates that neither case adequately represents reality. Perhaps a more satisfactory picture of the situation near monolayer coverage can be obtained by comparison with liquid diffusion. In that case there is no fixed lattice, and the activation energy for diffusion evidently must account for the whole complex process in which a hole is formed and a molecule jumps from its previous position into the vacancy. The correlation of motions of adjacent molecules in near-monolayer systems precludes an accurate description of the effect of adsorbate self-encounters on the surface transport rate. However, it appears safe to assume that no significant change in jump distance occurs from this effect. Rather, the meaning of the energy barrier for migration gradually changes from a simple one which requires consideration of only the adsorbent-adsorbate interaction to one in which motions of surrounding adsorbate molecules are also invdlved. Returning the fixed-site model, another important effect on surface transport should be the distribution of energies of binding to the surface. The heat of adsorption for many gas-solid systems decreases with C, evidently because of the progressive filling of sites of decreasing strength. One would expect that molecules which are more weakly bound to the surface would encounter smaller energy barriers, and consequently would be more mobile. Surface heterogeneity may therefore result in an increase of D, with C,, since the binding energy decreases as the surface is filled. In summary, a hopping model offers a reasonable qualitative description of surface transport in systems which display adsorption energies exceeding the thermal energy of translation. At low coverage transport proceeds by the jumping of molecules between adjacent surface sites. At high coverage neighboring molecules interact and the process bears some similarity to liquid diffusion. However, here a jumping mechanism still occurs with a jump distance that is about the same as in the low coverage case. The variation in surface diffusivity with coverage is probably due to progressive filling of sites of decreasing energy. A quantitative statement of this model can be developed as follows. Smith and Metzner (1964) have derived a general equation for surface transport by a hopping mechanism in which both the jump distance and frequency may vary with C,
Experimental Section The surface diffusion of adsorbed gases was measured by determining the contribution of adsorbed layer flow to the total flow of gas through the porous sample. Under experimental conditions, the mean free path of the gas molecules was always a t least ten times the mean pore diameter, and for this condition pore flow should obey the Knudsen equation
Here, R is the total jump frequency per unit area (sec-1 cm-2). To use the equation, particular forms must be chosen for A, and R. As discussed above it appears reasonable to neglect variations in A, with C,. If additionally R is assumed proportional to C, (constant v), then eq 4 reduces to Fick’s law with constant D, given by eq 3. To account for the change in D, with C, a different behavior of R is suggested. The jump frequency for a heterogeneous surface can be expressed as a distribution function, v ( C s ) , which is relat-
where PG’ is the gas-phase permeability and C is a constant characteristic of the pore space. For Knudsen flow PG’dMT should be independent of pressure, temperature, and the nature of the gas. In the present study He and N2 were assumed to exhibit negligible surface flow, and the total permeability of these was taken to represent flow through the voids. The surface transport of an adsorbed gas was assessed by subtracting
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Ind. Eng. Chem., Fundam., Vol. 13,No. 2, 1974
ed to R by
dR = u(C,) dC, R
=
~oc’u(C,) dCs
(5) (6)
A value of v(C,) refers to the jump frequency of the increment of molecules adsorbed in the neighborhood of concentration, C,. Substitution of eq 5 and the assumption of constant A, into eq 4 yields
The jump frequency of a single molecule is given, according to transition statd’theory, by
v =
(8)
yOe-EIRT
where Y O is the frequency of vibration of the adsofbed molecule normal to the surface, and E is the size of the energy barrier which separates adjacent surface sites. As the surface is filled up and lower energy sites are occupied, the energy barrier for migration can be expected to decrease. A useful quantitative measure of the binding energy is the differential heat of adsorption q. As a simple approximation it can be assumed that E varies linearly with q
E
(9)
= aq
Similar relatioris between an activation energy and a thermochemical energy change are known in reaction kinetics, as described by Boudart (1968). Combining eq 1, 7 , 8, and 9 gives
D,= -1 ,,0 s2 e-a9
RT
=
Doe-aqlRT
(10)
In summary, a model has been presented which describes surface transport as the jumping of adsorbed molecules between adjacent adsorption sites of different energy. The result (eq 10)is just a quantitative statement that the more strongly adsorbed molecules are less mobile. This equation includes both the concentration and the temperature dependence of the transport and relates the transport directly to the heat of adsorption. In order to test the model, an experimental study of the transport of C02, S02, and NH3 in porous glass was carried out. These systems were chosen as examples of strong adsorption on a heterogeneous surface.
from its total permeability PT’a gas-phase Knudsen flow permeability, as follows: nonadsorbed gases
P,’m = P,’I/MT
=
c
(12)
adsorbed gases
Sealant
To Vacuum
II Before evaluating eq 13, a correction was applied to C to account for blockage of pores by adsorbed material (see Gilliland, et al., 1958). Permeability measurements established the surface flow as a function of gas pressure gradient in terms of a surface permeability Ps’. T o find a surface diffusivity, local gassurface equilibrium was assumed, and adsorption isotherms were used to relate pressures to surface concentrations. A final step is to relate the surface transport through the entire sample to that which would occur across unit width of flat surface. For this purpose a uniform bore capillary model with surface “tortuosity” factor k, was used. The equation for surface flow is then
11
1
Sample Assembly ( S e e Inset)
11
\Thermostat
Figure 1. Permeation apparatus
I
where A and L are the cross sectional area and thickness of the porous sample and S is its total internal surface area. The quantity k,2 is not independently measurable. However, a similar factor kg2 can be defined using the theoretical equation for Knudsen flow in tubes (see Satterfield, 1970). In the present work kg2 was found to be 4.7 from He and N2 permeation experiments (described below). However, a slightly higher value of 6.6 was used for k,2 in order to remain consistent with previous work on transport in the same type of porous glass (Gilliland, et al., 1958, 1962). A disk of porous Vycor glass No. 7930, obtained from Corning Glass Co., was used as the sample. The following properties were determined by standard methods (see Perkinson, 1965): cross section = 1.22 cm2; length = 0.31 cm; specific surface area (by BET method using xenon) = 1.63 x lo6 cm2/g; apparent density = 1.50 g/cm3; void fraction = 0.28 cm3/cm3; mean pore diameter (based on cylindrical pores) = 46 A. The permeation apparatus is illustrated in. Figure 1. Essentially, it consisted of two gas reservoirs of equal volume, separated by the porous sample. The sample was installed in an undersized piece of Neoprene tubing. Flow rates of He, N2, C02, SO2, and NH3 were measured as a function of pressure level over the range 40-600 Torr at several different temperatures. Before starting a run with a new gas, the sample was evacuated a t less than 0.005 Torr and simultaneously heated to about 100°C for about 20 hr. To run an experiment, a gas was introduced, and the pressure drop across the sample was adjusted to a small fraction of the mean pressure, P. For the nonadsorbed gases, steady state was attained almost immediately; however, an hour or two was required for the adsorbed gases to reach steady state. After attainment of steady state, upstream and downstream pressures were measured as a function of time, and total permeabilities were calculated from these data. The volumes on either side of the sample were large enough that deviations from steady flow were unimportant. After all flow runs had been completed, the sample was removed, crushed, and adsorption was measured on the size fraction of 20-100 mesh particles. A standard volumetric apparatus was used, as described elsewhere (Per-
To Gas I n l e t
I .
0
I
100 200
300 400 500 600 700 P, torr
Figure 2. Permeabilities of five gases in porous glass
kinson, 1965). Besides the isotherms and their slopes, isosteric heats of adsorption were determined from the temperature dependence of the amount adsorbed (15) Results are described in the following section.
Results Total permeabilities, multiplied by d M T , are shown as a function of P in Figure 2 for the five gases used. The constancy of P,’dMT for He and Nz at 30°C is evidence for the Knudsen flow of these nonadsorbed gases. On the other hand, C02, S02, and NH3 which were appreciably adsorbed under experimental conditions exhibit permeabilities larger than those corresponding to Knudsen transport. This extra flow is attributed to.migration in the adsorbed layer. Isotherms for C02, SOz, and NH3 are shown in Figure 3. Monolayer coverage values were found using the closepacked model of Brunauer (1943)
area /molecule
= 1.09(m/p)z’3
(16)
where m is the mass of a molecule and p is the density of adsorbate as saturated liquid at the average of the two temperatures used. Isosteric heats of adsorption found from these isotherms are given in Figure 4. Monolayer Ind. Eng. Chem., Fundam., Vol. 13, No. 2, 1974 97
-“I 20
I
c
I
I
I
I
15
u i? 10
-5
-M(COt)-
-
3 110
I
I
11 5
12.0
1
I 12.5 qiRT
1
130
I
13.5
14.0
14.5
Figure 6. Surface diffusivity correlation for COz
a
R x
M
: Monolayer
A
= Adsorption Points = Desorption Points
*
-
Amount
-
i
0 2
100 2 0 0 300 400 5 0 0
0
:
600 700 800 900
I-
P , torr
n .
P
Figure 3. Adsorption isotherms for COz, SOz, and NH3
x
0”
Figure 7. Diffusivity correlation for SO2 I
;
1
I
I
I
1
A H V = Heat of
1 0
10 20 A M O U N T ADSO RBED, rnmole/g
i
30
Figure 4. Isosteric heats of adsorption as a function of surface coverage
--I
M
='Monolayer A m o l n t
’ MISO,) I
I
25 -
I
I:
2t+
0‘ c -1O‘C - 21‘C -34’c
Figure 8. Diffusivity correlation for SO2 in porous carbon. Data of Pope (1961)
03
0 5
10 15 2 0 A M O U N T ADSO RBED, r n m o l e / g
25
Figure 5. Surface diffusivities as a function of coverage values and heats of vaporization of adsorbate as saturated liquid are shown for comparison. Surface diffusivities calculated from eq 14 using the permeation and adsorption data of Figures 2 and 3 are given in Figure 5 . These all increase severhlfold with amount adsorbed, which varies from 0.3 to 1.3 times monolayer coverage. It is clear that there is no special behavior near monolayer coverage for these gases. A strong variation of D, with the differential heat of adsorption was predicted above, on the basis of a model accounting for the hopping of adsorbed molecules between 98
Ind. Eng. Chem., Fundam., Vol. 13, No. 2 , 1974
sites of different energy. A quantitative test of eq 10 is shown in Figure 6 for the COz data. Among the several differential heats of adsorption which can be defined, the isosteric heat was used in this correlation. A similar correlation for SO2 is shown in Figure 7 . In both cases the average deviation from the correlating line is about 5% of D,. Significant trends away from the correlating line cannot be distinguished in either case, and an error analysis indicated that all points agree with the correlation within experimental error. Equation 10 yielded a similar correlation with the ammonia data. With this success, published data of other investigators were correlated in terms of eq 10. Data of Pope (1961) on SO2 flowing through compacted Carbolac carbon at four different temperatures are shown in Figure 8. Measurements of Carman and Raal (1951) for CFzClz in silica powder are shown in Figure 9. Measurements by Russell (1955) in this laboratory on the flow of ethylene, propyl-
Table I. Summary of Data from Surface Diffusivity Correlations
D,,cm2/sec
a
Isosteric heat of adsorption, kcal/mole
0.037 0.018
CZH4 C3Hs i-C4Hla CFzC12
Glass Glass Glass Glass Glass Glass Silica
0.025 0.27
0.48 0.47 0.60 0.81 0.75 0.46 0.63
4.1-6.3 5.5-7.7 6.5-8.8 5.3-7 .O 6.3-7.5 5.9-7.1 6.5-7.8
SO2
Carbon
0.22
0.43
6.7-8.8
Gas
Solid
coz co, 3"
5
1.15 1.20
\
50
\
4-
n
0 0"
0.20
3 -
e .. 3 3 1'c A - 21 5'C 2-
-51 13
14
15
q / RT
Figure 9. Diffusivity correlation for CFZC12 in silica powder. D a t a of C a r m a n a n d Raal(l951)
ene, and isobutane in porous glass were also correlated successfully by this method. The constants, DO and a, and the mean deviations from each correlation are summarized in Table I. With all of the eight gas-solid systems listed in the table, no systematic deviations from the correlating equation were evident, and it appears that eq 10 is successful in correlating the data within experimental error.
Conclusion In summary, a model has been developed, based on earlier work by Carman (1956), DeBoer (1952, 1969), and Smith and Metzner (1964); it describes surface transport as the jumping of adsorbed molecules between adjacent sites of different adsorption strength. The strong concentration dependence of the surface diffusivity is attributed to a change in the adsorption strength with concentration; this is taken into account by using the heat of adsorption as a correlating parameter. The result, eq 10, is quite economical in using only two constants to represent both concentration and temperature effects for a given gassolid system. The model of independently hopping molecules ignores some difficult aspects of adsorption and migration. For example, the change in q with C, in porous materials may result from progressive filling of microcracks of atomic dimensions (see DeBoer, 1952, 1969); our equation is developed from the viewpoint of a smooth surface with various kinds of sites scattered across it. The success of our equation does not imply that an accurate description of surfaces was incorporated in its development. Rather, it indicates that the strength of adsorption is of fundamental significance in determining
Mean deviation from correlation 6% 4% 9% 15% 17%
10% 4% 8%
Ref This study This study This study Russell (1955) Russell (1955) Russell (1955) Carman and Raal (1951) Pope (1961)
surface mobility and that this can be expressed quantitatively using the surface diffusivity and the heat of adsorption.
Acknowledgment This work was supported in part by the National Science Foundation. G. P. P. was partly supported by a Proctor and Gamble Co. Fellowship. Nomenclature a = constant, defined by eq 9, dimensionless A = cross-sectional area of sample, cm2 b = width of flow path, cm C = constant characterizing Knudsen flow in porous sample C, = surface concentration, mole/cm2 D, = surface diffusivity, cm2/sec E = activation energy for surface diffusion kcal/mole k,, k , = "tortuosity" factors for gas and surface flows in porous media, dimensionless M = mass of a molecule, g M = molecular weight, g/mole; also denotes amount adsorbed at monolayer coverage, mmole/g N , , Ns = gas and surface flow rate, mole/sec, or mmole/ hr = pressure, Torr P = average pressure of two gas reservoirs, Torr PG',Ps', PT' = permeabilities for gas, surface, and total flows through porous material, mmole/hr-cm2-Torr q, qst = differential, and isosteric, heat of adsorption, kcal/mole R = jump frequency per unit area, sec-1 cm-2; also gas constant T = absolute temperature, OK x = distance coordinate, cm
e
Greek Letters A, = surface mean free path or jump distance, cm Y = jump frequency per molecule, sec-1 p = density,g/cm3
Literature Cited Babbitt, J. D., Can. J. Res., 28A, 449 (1950). Barrer. R. M., "Diffusion in and Through Solids," Chapter VIII. Cambridge University Press, London, 1941. Boudart, M., "Kinetics of Chemical Processes," Chapter 8, Prentice-Hall, Englewood Ciiffs, N. J., 1968. Brunauer, S., "Adsorption of Gases and Vapors," Vol. I , Princeton University Press, Princeton, N. J.. 1943. Carman, P. C., "Flow of Gases Through Porous Media," Chapter V . Butterworths, London, 1956. Carman, P. C., Raal, F. A., Proc. Roy. SOC., Ser. A , 209, 38 (1951). DeBoer, J. H.."The Dynamical Character of Adsorption," 1st ed., Chapter VI, Oxford University Press, London, 1952: 2nd ed, Chapter VI. 1969. Gilliland, E. R., Baddour, R. F.,Engel, H. H., A.I.Ch.E. J., 8 , 530 (1962). Gilliland, E. R.. Baddour, R. F.. Russell, J. L.. A.1.Ch.E. J., 4, 90 (1958). Horiguchi. Y . . Hudgins, R. PI., Silveston. P. L., Can. J . Chern. €ng., 49, 76 119711. Perkinson, G . P., Sc.D. Thesis. Massachusetts Institute of Technology, Cambridge, Mass., 1965. Pope, C. G.,Ph.D. Thesis, University of London, London, 1961 I n d . Eng. Chem., F u n d a m . , Vol. 13, No. 2, 1974 99
Russell, J. L.. Sc.D. Thesis, Massachusetts -Institute of Technology, -. Cambridge, Mass., 1955. Satterfield, C. N., “Mass Transfer in Heterogeneous Catalysis,” pp 4172, M.I.T. Press, Cambridge, Mass., 1970. Smith, R . K., Metzner, A. B., J. Phys. Chem., 68, 2741 (1964).
Weaver. J. A,. Metzner. A. B.. A.1.Ch.E. J.. 12. 655 11966)
Received for review M a y 22, 1972 Accepted J a n u a r y 14, 1974
Diffusion on Surfaces. I I . Correlation of Diffusivities of Physically and Chemically Adsorbed Species Karl J. Sladek,*’ Edwin R. Gilliland,2 and Raymond F. Baddour Department of Chemical Engineering. Massachusetts lnstitute of Technology, Cambridge. Mass. 02739
Surface diffusion of hjdrogen on platinum was detected by permeation of H2 and inert gases in porous Pt. Below 1 Torr at 60-75 C surface transport was substantial in comparison with gas-phase transport. Surface diffusivities D, were about cm2/sec and the activation energy was 5.7 kcal/mole. Comparison of these and literature values of D, showed a relation between D, and the heat of adsorption 4 . Three classes of behavior were found, and differences were attributed to differences in the type of gas-surface bonding. Numbers m were asshned to each bond type and a general correlation was produced, Ds = 0.016. exp[-0.45 q/mRT] cml2Jsec. Only three values of m were needed to correlate data from 30 gas-solid systems. The currelation represents 11 orders of magnitude in D, to within 1’/2 orders of magnitude.
The mobility of chemisorbed atoms and molecules is an important factor in heterogeneous catalysis, since surface reaction rates depend on encounters of chemisorbed reaction intermediates. The spreading of chemisorbed layers on several metals has been measured quantitatively. The surface migration of physically adsorbed molecules was discussed in the first paper in this series (Gilliland, et al., 1974), and a hopping mechanism was developed along with a correlating equation employing the heat of adsorption. One purpose of the present work was to extend these concepts to the case of chemisorption. A second purpose of this work was to attempt a correlation of surface diffusivities in different gas-solid systems. This idea arose from the observation that the small mobilities of chemisorbed molecules may be associated with their large energies of bonding to the surface, in contrast to the higher mobilities of less strongly bound physically adsorbed molecules. A third aspect of this work was the measurement of surface transport of hydrogen in porous platinum, a system of particular importance in catalysis. Past work on surface migration of chemisorbed atoms and molecules is reviewed next. In contrast to the extensive data reported for transport in physical adsorption systems, measurements of mobility in chemisorption systems are relatively few. Pioneering work in this field was done by Taylor and Langmuir (1933) axid Bosworth (1936), who measured the spreading of cesium, sodium, and potassium on tungsten. More recently, Gomer and coworkers (1957), using the field emission microscope, observed spreading of oxygen and hydrogen on tungsten and of hydrogen on nickel. A further study of hydrogen on nickel was carried out recently by Satterfield and Iino (1968), using a permeation method.
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In all of these investigations, results were reported as Fick’s law diffusivities, D,. The magnitudes of reported D, values range from 10-5 to 10-13 cm2/sec, usually considerably below those characteristic of physical adsorption cm2/sec. It was systems, which are typically 10-2 to suggested by Gilliland, et al. (1974), that concentration and temperature effects can be represented by
where q is a differential heat of adsorption, which characterizes the strength of bonding to the surface. Known values of DO,a, and q for chemisorption systems are summarized in Table I. In cases of dissociative adsorption, assumed for hydrogen and oxygen on metals, the value of q refers to adsorption from a hypothetical atomic gas and is equal to half the measured, molecular heat of adsorption, plus half the dissociation energy of the diatomic gas. While temperature effects have been investigated, in only one study was the effect of concentration explored. Bosworth (1935) found an increase in D, of potassium on tungsten of three orders of magnitude, for a two-order increase in surface concentration. Unfortunately, the heat of adsorption was not determined, and eq 1 cannot therefore be tested for this case. The increase in D, with coverage is, however, similar in direction, but much larger in magnitude than the concentration effects typically observed with physical adsorption. In summary, surface diffusion in chemisorption systems appears to be qualitatively similar to diffusion of physically adsorbed material, The diffusivities are much smaller and the concentration effects are stronger for the chemisorbed molecules. The data on chemisorbed material are limited in extent and are especially lacking in information on concentration effects. With this in mind, the study of a new system, hydrogen on platinum, over a range of surface concentrations, was begun. This system was chosen because of its importance in catalysis and also because it
